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Counterexample bank

Part C is won by knowing which tempting claims are false. 148 counterexamples; 85 free. The rest come with the Notes pack.

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#1 · Probability & Statistics › Hypothesis Testing

“A UMP test exists for every testing problem” — false

Counterexample: H₀: μ = 0 vs H₁: μ ≠ 0 for N(μ, 1)

The MP test for $μ > 0$ rejects for large X̄, for $μ < 0$ for small X̄; no single test is best against both.

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